NEW YORK — The case seemed to defy imagination, as horrific detail after sad footnote continued to unfold about the death of a child and an adoption that never really was.

But the fatal beating here earlier this month of 6-year-old Elizabeth (Lisa) Steinberg, apparently at the hands of her adoptive parents, has also emerged as a grim symbol that has reheated a longstanding debate between supporters of traditional agency adoption services and advocates of the growing practice of independent, or private, adoption.

Adoption agency spokesmen charge that Lisa's abuse and death Nov. 4 are gruesome proof of loopholes in an independent adoption system they say often fails to protect the interests of the adopted children. Defenders of private adoption reply that adoption agencies are anachronistic and jealous of the thriving business increasingly enjoyed by many independent adoption practitioners. The Steinberg case, they say, is a tragic example of child abuse that, as Bruce Rappaport of the Independent Adoption Center in Pleasant Hill, Calif., put it, "has nothing to do with adoption, anyway."

Both Face Murder Charges

Brought to an ironic light as the nation observes National Adoption Week, the strange facts of the Steinberg case centered on 46-year-old New York attorney Joel B. Steinberg and his longtime live-in companion, former children's book editor and author Hedda Nussbaum, 45, both of whom now face murder charges. State and county officials have failed to produce any evidence that adoption proceedings were completed for Lisa or for a second child, 16-month-old Mitchell.

But for opposing factions in the adoption arena, the controversy rapidly broadened beyond Lisa's death.

"Basically this debate has been raging certainly for 25 years," said Jim Brown, head of the adoption program for the State of California in Sacramento. Brown characterized the increasingly impassioned argument as involving "people more of a social services persuasion and people who advocate independent adoption who have each staked out views, largely stereotyping the positions of the others."

Debate 'Very Complicated'

"The debate gets very complicated, because historically both sides have made claims that go beyond the facts," said Peter W. Forsythe, vice president and director of the program for children at the Edna McConnell Clark Foundation in New York and long active in issues concerned with adoption. "It's easy to do that.

"I think it's important to point out that banning private adoption would not have affected the Steinberg situation," said Forsythe, who is also an attorney and an adoptive father, "because what Steinberg did was not an adoption."

At the National Committee for Adoption in Washington, which represents 140 adoption agencies nationwide, Jeff Rosenberg, director for adoption services, said that the Steinberg case "does point the way for some real change in independent adoption."

Attorney-arranged adoptions such as those of Lisa and Mitchell Steinberg bypass the preplacement screening that adoption agencies demand of prospective adoptive parents, he said, noting that no state licensing is required of lawyers or social workers involved in private adoption.

"I can't walk down to the corner here and sell hot dogs without some kind of certification from the state or the city," he said, "but I can walk down the street and arrange an adoption without being licensed."

"That's the agency argument," said David Leavitt, an attorney in Beverly Hills who handles 200-300 independent adoptions each year. "The agency says, 'We are licensed, we are qualified, we are better, everything else should be outlawed.' "

But increasingly, in Leavitt's experience, "birth mothers avoid agencies like the plague."

In a conventional agency adoption, a woman or a couple relinquishes a child to an agency, which in turn consigns the child to a couple it has interviewed and screened. The birth mother may see a list of potential adoptive parents for her child, but only in the case of a relatively new procedure, an identified adoption, will she know their exact identity.

Occasionally, because of delays in placement, the child may be sent temporarily to a foster home. But the procedure is considered final once the child is placed with the adoptive parents, since the birth mother has technically assigned rights to the agency rather than to the adopting parents.

In a private, or independent, adoption, on the other hand, a pregnant woman chooses a couple to adopt her baby from a list provided by an attorney, physician or independent adoption facility. In most cases, the pregnant woman meets the prospective parents of her child. Often, the adoptive parents are present at the birth. Medical fees and other fees are paid directly to the pregnant woman through her lawyer or her physician, not through an agency. Contact between the parties is generally encouraged, but finalization periods for these private adoptions vary from state to state.